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Main Title: Interconnected systems with uncertain couplings: explicit formulae for μ-values, spectral value sets and stability radii
Author(s): Karow, Michael
Hinrichsen, Diederich
Pritchard, Anthony J.
Type: Research Paper
Abstract: In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin type perturbations''). We derive explicit and computable formulae for the associated $\mu$-values. The results are then applied to characterize spectral value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case the classical eigenvalue inclusion theorems of Gershgorin, Brauer and Brualdi are obtained as corollaries. Moreover it follows that the inclusion regions of Brauer and Brualdi are optimal for the corresponding perturbation structures.
Subject(s): interconnected systems
spectral value sets
stability radii
Issue Date: 11-Mar-2005
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 93D09 Robust stability
93B60 Eigenvalue problems
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2005, 09
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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